solidarity, responsibility and group identity
TRANSCRIPT
Solidarity, Responsibility and Group Identity
Jano Costard
Friedel Bolle
___________________________________________________________________
European University Viadrina Frankfurt (Oder)
Department of Business Administration and Economics
Discussion Paper No. 309
December 2011
ISSN 1860 0921
___________________________________________________________________
Solidarity, Responsibility and Group Identity1 Jano Costard and Friedel Bolle
Discussion Paper 309, December 2011
Abstract: In the Solidarity Game (Selten and Ockenfels, 1998) lucky winners of a
lottery can transfer part of their income to unlucky losers. Will losers get smaller
transfers if they can be assumed to be (partly) responsible for their zero income
because they have chosen riskier lotteries (Trhal and Radermacher, 2009)? Or will
risk-lovers and risk-averters develop group identity feelings, leading to larger
transfers within, rather than between, the groups (Chen and Li, 2009, for charitable
transfers between and within otherwise defined groups)? In an experiment we find
behavior to be guided by in-group favoritism. Responsibility for self-inflicted
neediness does not seem to play an important role. In-group/out-group behavior is
successfully described by a variant of a social utility function suggested by Cappelen
et al. (2010).
Key-Words: Risky Behavior, Group Identity, Solidarity
JEL codes: D3, D8
Europa-Universität Viadrina Frankfurt (Oder)
Lehrstuhl Volkswirtschaftslehre (Mikroökonomie)
Postfach 1786
D - 15207 Frankfurt (Oder), Germany
Email: [email protected]
1 We would like to thank Hannah Liepmann, Annemarie Conrath, Alexandra Jung, Agnieszka Gryska and in particular Claudia Vogel for helping to conduct the experiment. Yves Breitmoser provided rather helpful advice with respect to statistical questions. Remaining shortcomings are, of course, ours.
2
1. Introduction
“Solidarity means a willingness to help people in need who are similar to oneself but
victims of outside influences such as unforeseen illness, natural catastrophes, etc.”
(Selten and Ockenfels 1998, p. 18; our emphasis).
Widespread solidarity is a form of insurance without explicit contracts. All types of
insurance, however, suffer from the problems of moral hazard and adverse selection.
Therefore, whenever possible, insurance differentiates between customers from
different risk classes and rules out payment in cases of gross negligence. Higher risk
groups receive less coverage or have to pay higher fees. It is a natural question
whether voluntary solidarity also differentiates between risk groups and/or people
who consciously decide to take higher or lower risks. Those who are ready to take
high risks may be held partly responsible if they fail - and therefore receive smaller
solidarity transfers. On the other hand, benefactors who also have taken risks (and
succeeded) may be more sympathetic to fellow risk-takers than to “scaredy-cats”.
The latter argument is supported by a vast amount of literature on the formation of
group identity, often with the consequence of in-group favoritism (Tajfel, 1970;
Kramer et al., 1993; Akerlof and Kranton, 2000, 2005; Güth et al., 2005; Bernhard et
al., 2006; Tan and Bolle, 2007; Charness et al., 2007; Ben-Ner et al., 2009). Further
literature is discussed in Chen and Li (2009).
Holding people responsible for their decisions and group identity feelings suggest
different types of solidarity behavior between people who decide to take a higher risk
and those who do not. According to the responsibility argument, people in need
would receive less help if they chose the more risky option. With group identity
feelings, however, lucky risk takers show more support for needy risk takers than
towards needy risk averters and vice versa. It is the aim of this paper to evaluated
the empirical relevance of these arguments
In experimental economics, solidarity has been mainly investigated in the framework
of the Dictator game and the Solidarity game. In the original Solidarity game of Selten
and Ockenfels (1998), the three members of a group are each endowed with DM 10
with 2/3 probability and with DM 0 with 1/3 probability. In the cases where there are
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winners (who got DM 10) and losers (who got nothing), the winner(s) can give an
arbitrary amount of their endowment to the loser(s). Further experiments investigate
the impact of the strategy method (Büchner et al., 2007), the influence of culture
(Ockenfels and Weimann, 1999), or are concerned with the identification of different
types of behavior (Bolle et al., 2012). We may regard the Dictator game as a two-
person solidarity game although it is rarely discussed under this aspect. It seems that
in the dictator game roles (rich and poor) are “given” while in the Solidarity game the
random mechanism which determines incomes (winners and losers) is emphasized.
In addition, for some purposes the three-player design has advantages. If the only
winner of a group determines his transfer to two different losers then we can directly
see whether and how they are treated differently.
An experiment closely related to ours is Trhal and Radermacher (2009), where the
original Solidarity Game (Solidarity Treatment ST) was conducted as well as another
experiment, called Risk Treatment RT. In RT each of the three participants of a
solidarity group had to choose between lottery C: “€10 with certainty” or lottery R: “€0
with Prob=0.5, €10 with Prob=0.4, €60 with Prob=0.1.” In RT, only winners of €10
were allowed to compensate losers. All subjects played both treatments, half of them
in the order (ST, RT) and half of them in the opposite order, each time in a newly
formed group. Trhal and Radermacher (2009) find that subjects in RT who voluntarily
took risks and failed, receive less compensation than subjects in ST who could not
avoid risks. Contrary to this finding is the observation of Buitrago et al. (2009) that
charitable giving in a variant of the Samaritan’s Dilemma game is not affected by the
question of whether neediness was self-inflicted or not.
Our paper will analyze giving behavior in a variant of the Solidarity Game which is
close to the Rademacher et al. (2009) design. However we will show that solidarity
transfers are heavily influenced by in-group favoritism as in Ben-Ner et al. (2009) and
Chen and Li (2009). Ben-Ner et al. (2009) find, among other results that giving in a
Dictator game is influenced by similarity of political views and belief in god. Chen and
Li (2009) define groups by preferences either for Klee or Kandinsky paintings. They
show that there is more altruism and less envy as well as more positive reciprocity
and less negative reciprocity between members of the same group than between
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members of different groups. In our paper group membership will be defined by the
level of risk-taking.
Cappelen et al. (2010) propagate a similar approach though they do not explicitly
refer to group identity feelings. In their experiment, subjects first have a binary choice
of either a riskless income or a lottery ticket. Then the ex-post aggregate income of
two randomly matched subjects can be redistributed by one of them or by a spectator
without own interests. Cappelen et al. (2010) find that the redistribution behaviour of
their subjects can be explained by subjects having one of three types of social utility
functions which are based on either one of two unconditional fairness norms or on a
conditional fairness norm. The latter implies discrimination of in-group and out-group
subjects where the risk-takers form one group and the risk-averters the other. We will
come back to this model in Section 3.
Why is there discrimination at all? According to Eaton et al. (2011), the origin of
group formation and in-group favoritism is the hunter-gatherer society in which
mankind for 99% of its existence has lived. In a group where food is at least partly
shared, risk averse individuals’ utility maximization requires supporting other risk
averse individuals who help to create a steady stream of food. On the other hand, if
someone is risk-prone he also would like his group to be risk-prone.
In the next section the experiment is described and in Section 3, following Cappelen
et al. (2010), a theory of redistribution is suggested. This order is preferable because
hypotheses can be formulated with respect to the specific experimental conditions. In
Section 4 the experimental results are discussed, and Section 5 concludes.
2. The Experiment
The experiment took place at the European University Viadrina in Frankfurt (Oder),
Germany, in 2009. 237 students from the faculties Economics and Business, Law,
and Cultural Sciences participated in the experiment. They were invited via email and
distributed into two sessions. Each session lasted about one hour. The subjects were
placed in a large lecture hall as in written exams, i.e. with so much space between
them that the six experimenters could prevent communication. All participants
5
received a show-up fee of €3. The experiment started by giving the participants an
instruction form and a first decision form.2 The instruction form explained that an
initial income would be created by one of two random processes (lottery tickets)
between which they could choose.
Random process A: With probability 2/3 you “win” €10, with probability 1/3 you
receive €0.
Random process B: With probability 1/3 you “win” €20, with probability 2/3 you
receive €0.
They were further told that they would be matched with two other (anonymous)
people in the room to form a group of three. If their group consisted only of “winners”
or “losers” (who receive €0) then the game would end. If it consisted of winners and
losers, the winner(s) could transfer arbitrary parts of their prize to the loser(s). After
receiving this general information the subjects chose A or B (knowing that there
would be a phase with voluntary transfers). They also reported their expectation
about the frequencies of A- and B-choices. Then they had to draw an A- or B-
envelope (according to their decision) from a box.3 By opening the envelope they
found a new decision form.
First they were informed that they were winners or losers. We deviated from a
complete strategy method because the winners had to decide among five further
conditions (see below). An additional fundamental conditionality (“if you are a
winner”) might have restricted the perceived relevance of decisions too much.
Because of the same reason we restricted the number of conditions to five. In the
following, those who have chosen A and lost (received €0) are called A-losers, the
others A-winners. B-losers and B-winners are defined respectively. The winners
decided on their transfers for the different possible loser structures and reported their
expectations about the other winner’s transfers in the one-loser case. Losers decided
on transfers “they would have made if they had been winners”. The losers’
hypothetical decisions served mainly to keep them busy and not to disturb the
winners. The participants were told that all payments would be carried out according
2 The English translation of both forms can be found under http://econ.euv-frankfurt-o.de/jc/Instruktionen.pdf 3 Within about five minutes, six experimenters with boxes distributed the new decision forms.
6
to the random matching of participants. They could collect their money later from a
person not involved in the experiment (after reporting their subject number and their
self-chosen pseudonym).
We required the winners to make conditional transfer decisions in five different
situations:
(T1) How much would you give to a single A-loser? 4
(T2) How much would you give to a single B-loser?
(T3) How much would you give to each of two A-losers?
(T4) How much would you give to each of two B-losers?
(T5) If there is one A-loser and one B-loser, how much would you give to the A-
loser and how much to the B-loser?
In the end they were asked to write a short comment on their decisions. In addition,
they reported their gender, faculty, semester and age.
3. Solidarity theory
In the one winner/two losers case we generalize the two-person social utility function
of Cappelen et al. (2010) in the following way:5
(1) XFyXFyyV hkhi
jkjiii
2/)(2/)( 2)(2)( −−−−= ββγ
iy is the income which winner i reserves for himself and jy and hy are the losers’
incomes, i.e. i’s transfers to them. hji yyyX ++= is i’s prize (€10 or €20). is a
general and is an individual positive parameter. )( jkF is an individual fairness
standard for j’s income which can take one of three forms. For a share of the
population the ex post standard “equality of income”, i.e. 3/XF EP = , is assumed to
be fair; for a share it is the ex ante standard “equality of opportunity”. As
everybody has the same options he or she should keep his income, which means for
losers 0=EAF . For a share a conditional fairness standard
4 I.e. there are two winners and one loser. In order not to introduce further ramifications of the hypothetical decisions, the type of the other winner is not revealed. 5 The only important difference is the second loss term.
7
applies: is fair if i and j both have chosen the same lottery ticket and is fair
otherwise. This social utility function yields the following forecast.
(2) },0max{)(
i
jkj
XF
Xy
βγ
−=
and correspondingly for loser h. 3/10/)( orXF jk = implies that, ceteris paribus, A-
and B-winners should transfer the same share of their prize, but they differentiate
between in-group and out-group transfers. Out-group transfers under the standards EAF and CEF are always zero.
If there is one loser j and a second winner h then, from i’s point of view,
(3) XEFyEXEFyEyV ihk
hiiijk
jiiii 2/)(2/)( 2)(2)( −−−−= ββγ
hiiji tEtyE += is the loser’s expected income after i’s transfer it and h’s expected
transfer hi tE . The “ex post” fairness standard is defined as 3/XEF iEP = with
(4) )3/()1(*20' iii prizelotterysiXE αα +++= ,
with iα = i’s expected share of A-players6. i’s maximization of (3) yields
(5) }/,0max{)(
ii
hi
i
jk
i
i
XEtE
XEF
XEt
βγ−−= .
While the estimated shares of A-players are nearly the same (66% and 63% for A-
and B-winners) the expectations hitE are rather different. A-winners expect on
average transfers of €1.82 and B-winners €2.85. The difference is highly significant
(p<10-7 in a two-sided Mann-Whitney U-test). In relation to EiX, however, we find
6 The conditional probability that the only other winner is an A-winner is
)31/(4)9/)1(9/4/()9/4( iiiii ααααα +=−+ .
8
(6) )/( XEEtaverage ih = 0.0997 for A-winners and 0.0992 for B-winners.
Therefore we expect the same result as in the two-loser case, however in terms of
shares of XEi : If there are no further differences between A- and B-players then
they should transfer the same shares of XEi .
Using the elicited expectations of the other winner’s transfer in this way implies the
hypothesis that, first, subjects develop expectations, and then they decide on
transfers based on these expectations. Alternatively, we can assume that the two
winners determine the Bayesian equilibrium of the “public good” game they play. (In
the case of interdependent utility functions the income of the loser is a public good or
bad for the winners.) We could not use the expectations as in (4) if the winners
determine the transfers first (with whatever rationale) and then determine their
expectations on the basis of their own transfers. For a discussion of this problem see
Selten and Ockenfels (1998).
Under the ex ante fairness standard, transfers should be zero.
We define τi→j = average transfer as share of EiX from winner type i to the (only)
loser of type j. We expect in the two winners/one loser case average transfers with
the following relations:
Hypotheses 1. τA→A = τB→B (in-group transfers)
2. τA→B = τB→A (out-group transfers)
3. (a) τA→B ≤ τA→A
(b) τB→A ≤ τB→B (in-group vs. out-group transfers)
All transfers of those subjects with the standard EAF (=0) as well out-group transfers
of subjects with the fairness standard CEF are zero. In addition, also subjects with a
fairness standard EPF may transfer nothing if they are not inequality averse enough
or if they expect a too large7 transfer by the other winner. Let us assume that their
7 (4) implies the crowding-out of solidarity transfers (which are strategic substitutes), other social utility functions can imply crowding-in (see Bolle et al., 2012).
9
shares are Aδ and Bδ . Then, in the two winner/one loser case, the share of zero
transfers is )( EPCEA
EA λλδλ ++ for in-group transfers from A-winners to A-losers and
)( EPCEB
EA λλδλ ++ from B-winners to B-losers. The share of zero out-group transfers
from A-winners to B-losers is EPA
CEEA λδλλ ++ , and the share of zero out-group
transfers from B-winners to A-losers is EPB
CEEA λδλλ ++ . Because of (6) we expect
AB δδ = . With the definition ϕ i→j = frequency of zero transfers from winner type i to
the (only) loser of type j we expect
Hypotheses 4. ϕA→A = ϕB→B (in-group transfers)
5. ϕA→B = ϕB→A (out-group transfers)
6.(a) ϕA→A ≤ϕA→B (in-group vs.
(b) ϕB→B ≤ϕB→A out-group transfers)
In the one winner/two losers case we define τi→jh = transfer (as share of i’s prize) of
winner type i to a loser of type j, when the other loser is of type h. ϕ i→jh is defined
correspondingly.
Hypotheses 7. (a) τA→AA =τB→BB (b) τA→AB =τB→BA (in-group transfers)
8. (a) τA→BB = τB→AA (b) τA→BA = τB→AB (out-group transfers)
9. (a) τA→AA ≥ τA→BB (b) τB→BB≥τB→AA (in-group vs.
(c) τA→AB ≥ τA→BA (b) τB→BA ≥ τB→AB out-group transfers)
10. (a) ϕA→AA = ϕB→BB (b) ϕA→AB = ϕB→BA (in-group transfers)
11. (a) ϕA→BB = ϕB→AA (b) ϕA→BA = ϕB→AB (out-group
transfers)
12. (a) ϕA→AA ≤ ϕA→BB (b) ϕB→BB ≤ ϕB→AA (in-group vs.
(c) ϕA→AB ≤ ϕA→BA (d) ϕB→BA ≤ ϕB→AA out-group transfers)
4. Results 230 of the 237 participants delivered completely filled questionnaires. Among these
there were 60% female students. The faculties were represented with 60%
economics and business students, 15% law students and 26% cultural science
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students. It is remarkable that only 47% of our subjects chose the less risky A and
53% the more risky B lottery. On the first glance this seems to be an astonishingly
high number of risk seekers. In Cappelen et al. (2010), for example, 90 percent of the
subjects preferred a riskless income to a risky lottery with the same expectation
value. Note, however, that this difference is at least partly caused by the well-known
certainty effect. (See, for example, Cohen and Jaffray, 1988.) Another reason for so
many risk seekers might be that they are somewhat insured by the expected
solidarity transfers. In a follow-up investigation by Lübbe and Bolle (2011), however,
it is shown that moral hazard does not play a significant role for the choice of B. It is
also interesting to note that the average expectations of the frequencies of B-choices
are 35% which is less (p=0.07 in a chi square test) than the real choices of B but
which is still large if one expects most people to be risk averse.
Men and economists chose slightly, but not significantly more often (about 10
percentage points), the riskier B-lottery. In the end, we had 73 A-winners and 35 B-
winners, which are the basis of the following analysis. Only 5 of these 108 decision
makers (4%) did not collect their money. The average transfers of A-winners to A-
losers, €1.27 in the one-loser case and €1.13 in the two-loser case are close to those
in treatment ST of Trhal and Radermacher (2009).
4.1 Aggregate Results
The average relative amounts which losers receive are presented in Table 1. In the
one winner/two losers case the expected group income Ei(X) is equal to the prize
which the only winner receives. The simple result is strong discrimination: In-group
transfers are between 10.8% and 12.7% of the winner’s prize. Out-group transfers
are between 7.0% and 8.8% of the winner’s prize. Hypotheses 3 and 9 are strongly
supported (only for the comparison of τB→B and τB→A measured as shares of EiX the
level of significance is lower). Also Hypotheses 1, 2, 7 and 8 are supported as no
significant differences (p<0.05) between the comparable transfers are found.
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Transfer types Transfers (stand. dev.) in % of
prize EiX
N
Two winners
and one loser
τA→A
τA→B
12.7* (11.3) 6.7* (5.9) 7.2 (9.3) 3.8 (4.9)
73
τB→B
τB→A
11.3* (11.8) 8.3+ (8.6) 8.8 (11.4) 6.4 (8.3)
35
One winner and
two losers
τA→AA
τA→BB
τA→AB
τA→BA
11.3* (9.1) 6.8 (7.9)
12.4* (9.9) 7.0 (8.1)
73
τB→BB
τB→AA
τB→BA
τB→AB
9.6* (10.8) 7.1 (7.7)
10.8* (12.0) 7.0 (8.1)
35
Table 1: Relative transfers from winners to losers (in-group transfers in bold type).
In-group/out-group differences: *(+) Significantly larger than the value in next line
according to a Wilcoxon matched pairs signed rank test with p < 0.01 (p=0.06).
Table 2 presents frequencies of zero transfers under two definitions of zero, namely
“exactly 0” and “< 10% of prize”. As the resulting differences are not “too large” we
can expect to arrive at similar conclusions also for other definitions of zero transfers.
With one exception (indicated by §) the in-group frequencies of zero transfers of A-
winners are not significantly different from the corresponding frequencies of B-
winners. This exception contradicts Hypothesis 10 (b), but it is the only contradiction
at all. In all cases the in-group frequencies of zero transfers are smaller than the
corresponding out-group frequencies. Only the transfers of A-winners, however, are
significantly different. While, for A-winners, the differences according to the definition
“exactly 0” are 51-33=18, 41-23=18, and 40-22=18, the corresponding differences for
B-winners are 46-37=9, 43-37=6, and 40-37=3. So it may be that, among A-players,
the conditional fairness norm is more frequent or “stricter” than among B-players. On
the other hand, we have seen in Table 1 that B-players differentiate enough (i.e.
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necessarily in the case of non-zero transfers where there should not be differences)
to make average contributions significantly different. This is an indication that A-
players and B-players might indeed be different. We will investigate this question in
the subsection 4.3.
Transfer types Share of zero transfers in %
Exactly 0 (<10%)
N
two winners
and one loser
ϕA→A
ϕA→B
33* (38*) 51 (58)
73
ϕB→B
ϕB→A
37 (51) 46 (60)
35
One winner and
two losers
ϕA→AA
ϕA→BB
ϕA→AB
ϕA→BA
23* (37**) 41 (60)
22* (29**) 40 (59)
73
ϕB→BB
ϕB→AA
ϕB→BA
ϕB→AB
37 (51) 43 (58)
37 (51§)
40 (63)
35
Table 2: Share of zero transfers (in-group transfers in bold type) measured as
“exactly 0” or in brackets as “smaller than 10% of endowment”. In-group/out-group
differences: * (**) significantly smaller than the corresponding value in next line
(Fisher exact probability test, p < 0.05 (0.01)). In-group/in-group difference: § significantly larger (Fisher test, p < 0.05) than ϕA→AB (29%).
4.2 Regression Analysis We extend our analysis by controlling for influences of individual attributes in a
regression analysis with the dummy variables 1w = 1 for women, 1Econ =1 for
economists, 1AB =1 if the transfer is from an A-winner to a B-loser, and 1BA and 1BB
respectively. The first line of Table 3 shows the results for the case where there is
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one loser. The value of the constant, 1.22 is the average amount which a male, non-
economist A-winner transfers to an A-loser. The regressions show that, compared
with the male non-economist, females’ transfers were on average €0.55 larger and
the transfers by economic students on average €0.57 smaller. Also, the coefficient of
the dummy 1AB is negative and significant, showing that A-winners transfer less to B-
losers than to A-losers. When interpreting the coefficient of 1BA one has to keep in
mind that B-winners won double the amount of A-winners, so a coefficient of zero
would mean that B-winners transferred on average and in relative terms only half as
much to A-losers than A-winners did. Further, the coefficient of 1BB being larger than
coefficient of 1BA indicates that B-winners favor B-loser over A-losers. This group
effect is stable over all winner/loser cases. Therefore, the regression analysis
confirms all the results from Table 1.
Const. 1w 1Econ 1A B 1B A 1BB Adj. R2
Two winners /one
loser
1.22 (0.000)
0.55 (0.01)
-0.57 (0.02)
-0.54 (0.03)
0.67 (0.04)
1.17 (0.000)
0.15
One winner /two
losers of same type
1.15 (0.000)
0.39 (0.03)
-0.51 (0.008)
-0.45 (0.03)
0.45
(0.09)
0.96 (0.000)
0.15
One winner /two
losers of diff. type
1.26 (0.000)
0.34
(0.08)
-0.46 (0.03)
-0.53 (0.02)
0.34
(0.28)
1.06 (0.000)
0.12
Table 3: Regression analysis of absolute transfers from a winner to the only loser/to
one of the two losers. N=216. In brackets p-values of a two-sided t-test8.
4.3 Structural modeling At last we want to investigate the model of Section 3 and the question of whether A-
and B-players have different preferences beyond their risk attitudes with a random
utility approach (McKelvey and Palfrey R., 1995). We concentrate on the one
winner/two losers case because we want to avoid the discussion mentioned in
Section 3 about the nature of the expectation formation in the two winners/one loser
case. We add a random term iε to the utility function (1), i.e.
8 The significance of dummy variable coefficients has been checked by additional incremental F-tests.
14
(8) ihk
hijk
jihjhjk XFyXFyyyXyyV
iεββγ +−−−−−−= 2/)(2/)()(),( 2)(2)(
and assume that iε is i.i.d. extreme value. The individual choice probabilities then
have a logit form. Following Cappelen et al. (2010) we assume iβlog to be normally
distributed with logβ i ∼ N(µ, σ).
jy is equal to τi→jh and hy is equal to τi→hj because i’s transfers are the only income
of j and h. The winners’ transfers could not be more than half of their prize and only 8
of the 432 transfers were not a multiple of 50 Eurocent. Thus we choose finite sets of
possible transfers (in Euro) to one loser, namely T=TA= {0, 0.5, 1.0, …., 5.0} for A-
winners and T=TB= {0, 0.5, 1.0, …, 10.0} for B-winners. The eight deviating values
are set equal to the closest element of the finite sets.
i’s decisions under the three conditions == hj yy τi→AA, == hj yy τi→BB, and ( jy =
τi→AB, hy = τi→BA) lead to utilities )(AAV ki
, )BB(ki
V , )AB(ki
V . The expected likelihood
of these three decisions is9
(9) == →→→→→ ),,;,,,, ( BAiABiBBiAAiAAi σµγτττττki
ki LL
),()),(exp()),(exp()),(exp(
))(exp(*))(exp(*))(exp(
0*),(
σµdFzyVyyVyyV
ABVBBVAAV
Ty Ty TTzy
kkk
kkk
iii
iii∫ ∑ ∑ ∑∞
∈ ∈ ∈
where F is the lognormal distribution. We assume the fairness standard k=EA to be
present in the population with a share of EAλ , standard EP with EPλ and standard CE
with EPEACE λλλ −−= 1 . Then the average likelihood of the three decisions is
(10) CEi
EPEAEPi
EPEAi
EAi LLLL )1( λλλλ −−++= .
9 γ can be assumed as the parameter of the logit equilibrium and βi/γ as the parameter of the normalized utility function.
15
In order to find out whether A- and B-players are different we estimate the
parameters ),,,,( EPEA λλσµγ for A- and B-players separately and jointly (Table 4).
The reduction of the log-likelihood score of 16.0 after adopting separate estimates
surpasses the critical limit described by the BIC and the AIC criteria. The
improvement is also highly significant in a likelihood ratio test (p= 4*10-5). The
differences between A- and B-players are mainly the different shares with which the
fairness standards are distributed. While A-players have more often (9.3 and 14
percentage points more) fairness standards EP and CE, the fairness standard EA is
more frequent (23.3 percentage points more) among the B-players. We can interpret
γ as the precision parameter of the logit choice probabilities; dividing the utility
function by γ delivers a normalized utility function whose only parameter β i/γ is
lognormal distributed with µ-log(γ) and σ. The distributions of β i/γ have the same µ-
log(γ) value and the same σ for A- and B-players but the B-players have a smaller γ
which indicates a larger random variance of behavior.
γ µ )log(γµ −
σ EAλ EPλ CEλ
-log(L)
A-players 3.13
(0.26)
2.73
(0.09)
1.68 0.19
(0.04)
0.22
(0.05)
0.60
(0.06)
0.18 429.3
B-players 1.34
(0.20)
1.99
(0.15)
1.70 0.19
(0.11)
0.46
(0.10)
0.51
(0.10)
0.04 274.1
A- and B-
players
2.26
(0.18)
2.43
(0.08)
1.42
0.34
(0.05)
0.26
(0.06)
0.60
(0.05)
0.14 434.8
+ 281.6
Table 4: Parameter estimation for (9) and (10) with the utility function (8)
We are not completely satisfied with this result, however. The small share of players
with a conditional (CE) fairness standard cannot explain the in-group/out-group
discrimination identified by non-parametric tests. We think that the EA fairness
standard and the CE out-group standard need not require strictly zero transfers.
While the fairness standard EP (equality) seems to be well rooted in society, we are
skeptical with respect to a standard of giving nothing (though actually many people
16
give nothing), not even in cases of “self-inflicted harm”.10 Therefore we introduce,
instead of zero standards, variable standards fEA∙X (X=prize) and fCE∙X (for out-group
players) in the utility function (8).
The estimated parameters are reported in Table 5. The separate estimation for A-
and B-players again significantly improves the log-likelihood score with respect to all
criteria (p=5*10-5 in the likelihood ratio test). The same is true when we compare the
scores of A-players (B-players) with and without the variable fairness standards. In
the likelihood ratio test we get p= 5*10-7 (p=10-10). Also the theoretical and empirical
frequencies of transfers are in good accordance (see Appendix) though they might
be further improved by introducing prominence (integer number transfers). Because
of the restricted number of B-winners, however, we did not want to extend the
number of parameters.
γ µ )log(γµ −
σ fEA fCE EAλ EPλ
CEλ -log(L)
A-pl. 2.54
(0.27)
2.58
(0.12) 1.68
0.38
(0.07)
-0.38
(0.25)
0.22
(0.02)
0.22
(0.05)
0.22
(0.08) 0.56 414.8
B-pl. 0.91
(0.22)
1.52
(0.31) 1.61
0.51
(0.16)
-4.64
(5.51)
0.27
(0.04)
0.33
(0.26)
0.00
(0.39) 0.67 252.1
A-
and
B- pl.
1.95
(0.20)
2.35
(0.13)
1.68
0.30
(0.06)
-0.66
(0.87)
0.23
(0.01)
0.27
(0.07)
0.25
(7.5) 0.48
421.1
+
263.6
Table 5: Introducing variable fairness standards FSEA= fEA and FSEA= fCE (out-group standard).
We find now - in accordance with the non-parametric tests – the majority of the
players deciding conditionally, i.e. showing in-group/out-group discrimination. They
feel an obligation to help also the out-group losers, however with a mild reduction of
their standard of transfers to a quarter (0.22, 0.27) of their income instead of a third
as in the case of in-group losers. The share of players with an ex post (equality)
standard is estimated as 22% for A-winners and 0% for B-winners, although in the
10 Think of the biblical Parable of the Lost Son (Luke 15, 11-32)
17
latter case with a large standard deviation. This is understandable because the
conditional decision makers and those with an ex post standard are, in particular in
the case of B-winners, not very different.
Surprisingly there are negative fairness standards in the group with an ex ante
standard which make zero transfers almost certain11. Because of the large standard
deviation we cannot say much more than that the standard is negative. But we can
say that these people are strong unconditional supporters of the idea that everybody
who had had his chance should care for himself12.
5. Conclusion The main regularity in Tables 1 and 2 is that risk averters (A-players) strongly favor
risk averters and risk seekers (B-players) weakly favor risk seekers. In-group
favoritism is also found in a regression analysis which controls for the influence of
gender and faculty. (Men and economists give less.) The result is further supported
by the estimation of social utility functions with more than half of the subjects using a
conditional fairness standard implying in-group favoritism. Our explanation of this
result is that risk taking behavior is a strong enough trait to evoke group identity
feelings, in particular among risk averters. The literature on the formation of group
identity shows even weaker attributes to be effective (Tajfel, 1970, and Chen and Li,
2009). Our results are qualitatively in line with Chen and Li (2009). In their
experimental investigation with charitable giving but with groups defined by
preferences for Klee or Kandinsky paintings, in-group beneficiaries received 47%
more than out-group beneficiaries. In our experiment in-group favoritism is between
28% and 79%. Our results are also in line with Cappelen et al. (2010) whose
suggested utility function describes – after a slight adaption – also the behavior of our
subjects. Note that while Cappelen et al. (2010) investigate redistribution of
aggregate income (in real situations by taxes and social insurance schemes) our
11 For A-winners with a fairness standard fEA=-0.38 we get prob(transfers=0)=0.98 in the case of two losers of the same kind and prob(transfers=0)=0.94 in the case of one A- and one B-loser. For B-winners with fEA=-4.64 the corresponding probabilities are 0.99997 and 0.997. 12 The elder brother of the Lost Son is strictly opposed to his father’s forgiving and joyful welcoming of the “loser”. He might be interpreted as having an EA-standard. His father, on the other hand, indicates that he is discriminative (CE-standard), telling his elder son “… everything I have is yours” (Luke 15, 31). The enthusiastic welcome, however, shows that the younger son need not fear really severe discrimination.
18
frame and focus is the voluntary transfer of income from “winners” to “losers” (within
the family, among friends, and by private welfare).
We find significant differences between A- and B-winners in our analysis of behavior
in the framework of a random utility approach, in particular concerning the precision
parameter of the decision probabilities and A- and B-players’ frequencies of the
fairness standards. The seemingly large difference of the EA out-group standard
makes almost no difference in terms of behavior. Both standards imply the almost
certain choice of zero transfers. B-players’ risk taking is accompanied less often by
the EP fairness standard and more often by the “equal opportunity” EA standard and
the conditional CE standard, i.e. risk takers reveal (and accept?) more often that
losers “do not deserve” transfers and they use more often a conditional fairness
norm. Our analysis estimates a conditional fairness standard fCE ≈ 1/4 for outgroup
players which is only a mild reduction of the fairness standard fEP =1/3 for ingroup
players. The different fairness standards and the different frequencies of fairness
standards in the population are the major differences to Cappelen et al. (2010), which
may be explained by the different nature of the redistribution in the two papers:
redistribution of aggregate income in Cappelen et. al. (2010) and transfers from one’s
own income in this paper.
Arguments for the evolutionary stability of in-group favoritism (Eaton et al., 2011) can
easily be extended to capture groups defined by risk preferences. That does not
mean that there are no alternative explanations. We may assume that A-winners can
easier imagine themselves in the shoes of A-losers and that therefore empathy is
easier evoked than in the case of B-losers (and vice versa). These are not
completely different explanations, however, because ease of empathy can be
regarded as a possible (or even the most important) determinant of group identity
feelings.
It is only natural that A-winners accuse B-losers of “irresponsible” behavior. In their
free comments, 33 of 73 A-players did so13. Only one of the 35 B-players, however,
expressed this opinion. Behavior seems to be denounced as irresponsible only if it is
riskier than one’s own. 9 B-players explicitly remark, that B-losers should get more 13 They do not always use the term “irresponsible“ but they express their opinion that the B-players should not have chosen such high risk.
19
transfers because they are more risk-loving (i.e. like themselves). Even this
condensed report about the free comments seems to indicate that in-group
favoritism/out-group aversion is differently strong between A- and B-players. A-
players condemn the decision of B-players more often and more fiercely than vice
versa. Thus we may ask whether there are move differences between B-players and
A-players than those which we have identified in our paper.14
We think that it is worthwhile to look for more differences in further studies. In a world
beyond our simple model there may be more agreement about the question when
risk takers should be called irresponsible (risk loving car drivers) or beneficial for the
society (entrepreneurs with innovative products or processes). The relatively large
share of players with an unconditional ex ante (equal opportunity) standard among B-
players shows that many people take high risks without expecting solidarity. The size
of this group probably depends on circumstances.
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Economics, 115, . 715-753.
Akerlof, G. and Kranton, R. E. (2005), "Identity and the Economics of Organizations",
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Ben-Ner, A., McCall, B.P., Stephane, M. and Wang, H. (2009), "Identity and In-
Group/Out-Group Differentiation in Work and Giving Behaviors: Experimental
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Bolle, F., Breitmoser, Y., Heimel, J., Vogel, C. (2012), "Multiple Motives of Pro-Social
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10.1007/s11238-011-9285-0.
Büchner, S., Coricelli, G., Greiner, B. (2007), "Self Centered and Other Regarding
Behavior in the Solidarity Game", Journal of Economic Behavior and
Organization, Vol. 62, Issue 2, pp. 293-303.
14 Neither do A- and B-players differ significantly with respect to their share of women or economists. In the follow-up study by Lübbe and Bolle (2011), however, differences according to a personality test are found.
20
Buitrago, G., Güth, W. and Levati, M.V. (2009), "On the Relation between Impulses
to Help and Causes of Neediness: An Experimental Study", The Journal of
Socio-Economics 38, 80-88.
Cappelen, A.W., Konow, J., Sørensen, E.Ø., Tungodden, B. (2010), “Just Luck: An
Experimental Study of Risk Taking and Fairness”, NHH Discussion Paper
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Membership", American Economic Review 97 (4), 1340-1352.
Chen, Y. and Li, S.X. (2009), "Group Identity and Social Preferences", American
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Cohen, M., and Jaffray, J.-Y. (1988), "An Experimental Analysis of Decision Making
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Performance 14 (4), 554-560.
Eaton, B.C., Eswaran, M., Oxoby, R. (2011), "'Us' and 'Them': The Origin of Identity,
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Fehr, E., and K. Schmidt. (1999), “A Theory of Fairness, Competition and
Cooperation”, Quarterly Journal of Economics, 114(3): 817-68.
Kramer, R.M., Pommerenke, P., Newton, E. (1993), „The social context of negotiation
- effects of social identity and interpersonal accountability on negotiator
decision making”, Journal of conflict resolution 37 (4), 633-654.
Lei, V., and F. Vesely. (2010), “In-group vs. Out-group Trust: The Impact of Income
Inequality”, Southern Economic Journal, 76(4): 1049-1063.
Lübbe, I. and Bolle, F. (2011), “Who helps whom? Risk Taking and Solidarity in a
Virtual World”, Discussion Paper 210, Europa-Universität Frankfurt (Oder),
December 2011.
McKelvey, R. D. and T. R. Palfrey R. (1995) “Quantal Response Equilibrium for
Normal Form Games,” Games and Economic Behavior, 10, 6-38.
Ockenfels, A. and Weimann, A (1999), “Types and patterns: an experimental East-
West-German comparison of cooperation and solidarity" in: Journal of Public
Economics 71, 275–287.
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21
Trhal, N., Radermacher, R. (2009), "Bad Luck vs. Self-Inflected Neediness – An
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Appendix: Theoretical and empirical transfers.
Figure 1: A-winners’ transfers to two A-losers. 73 data points.
Figure 2: A-winners transfers to two B-losers. 73 data points.
22
Figure 3: A-winners’ theoretical transfers to one A-loser (backward pointing axis) and
one B-loser (forward pointing axis). 73 data points.
Figure 4: A-winners empirical transfers to one A-loser (backward pointing axis) and
one B-loser (forward pointing axis). 73 data points.
23
Figure 5: B-winners transfers to two A-losers. 35 data points,
Figure 6: B-winners transfers to two B-losers. 35 data points.
24
Figure 7: B-winners’ theoretical transfers to one A-loser (backward pointing axis) and
one B-loser (forward pointing axis). 34 data points.
Figure 8: B-winners’ empirical transfers to one A-loser (backward pointing axis) and
one B-loser (forward pointing axis). 34 data points.
25
For online publication! General Instructions (Translation from German) For the following experiment, you can influence your initial endowment (in Euro) by
choosing between two random processes.
Random process A: With probability 2/3 you “win” Euro 10, with probability 1/3 you
receive Euro 0.
Random process B: With probability 1/3 you “win” Euro 20, with probability 2/3 you
receive Euro 0.
After choosing the initial endowment, groups of three are built by random choice from
the attendees. If a group consists only of winners or only of losers, the game ends. If
the group consists of one or two winners, each winner has the possibility give money
to the loser(s). You will be informed on the chosen alternative of the “loser”, but won’t
get information on the choice of the second winner in case there are two winners.
You receive the money that results from your decision. If you are a loser, you
receive, in addition to your initial endowment, the money the winner(s) transfer to
you. If you are a winner, you receive your initial endowment minus the transfers to
the loser(s).
You can collect your payoff from ……….. to …………… in room ………. Please
remember your number and pseudonym!
26
Number: Pseudonym: ________________ Which of the alternatives do you choose? Random process A: With probability 2/3 you “win” Euro 10, with probability 1/3 you
receive Euro 0.
Random process B: With probability 1/3 you “win” Euro 20, with probability 2/3 you
receive Euro 0.
Please check the alternative with which your initial endowment should be
determined:
Random process A
Random process B
What do you think, how many of the attendees pick random process A? How many
pick random process B?
Random process A is choosen by ____________ % the attendees.
Random process B is choosen by ____________ % the attendees.
27
Case: Subject has chosen A and won.
Number: Pseudonym: ________________ You were determined by the random process to be a „winner” and you received an
initial endowment of Euro 10.
(a) What will you give if there are two winners in your group and you have no
information on the other winner?
Answer A: To a loser, who chose random process A,
I give __ _,__ _ €.
Answer B: To a loser, who chose random process B,
I give __ _,__ _ €.
What do you expect the others to transfer on average? (The best estimation will be
rewarded with €10, each)
Answer A: I expect __ _,_ __ € on average for a loser, who chose
random process A.
Answer B: I expect __ _,_ __ € on average for a loser, who chose
random process B.
28
(b) What will you give if you are the only winner in your group?
Answer A: In case both losers chose random process A,
I give each of them __ _,__ _ €.
Answer B: In case both losers chose random process B,
I give each of them __ _,__ _ €.
Answer C: In case one loser chose random process A and the other loser chose
random process B,
I give the one who chose random process A __ _,__ € and
the one who chose random process B __ _,__ €.
(c) Personal data
Sex: □ male □ female
Faculty: □ Economics/Business □ Law □ Cultural Science
Age: __________ Semester (overall): __________
In case your transfers differed between losers who choose A and losers who choose
B, please comment on the reason.
29
Case: Subject has chosen B and won Number: Pseudonym: ________________ You were determined by the random process to be a “winner” and you received an
initial endowment of Euro 20.
Otherwise: same questions as to A-winners.
Cases: Subject has chosen A or B and lost (data not analyzed) Number: Pseudonym: ________________ You were determined by the random process to be a “loser”.
What do you think, how much do you get from the winner(s)?
In case there are two winners, I receive altogether ___ _ €.
In case there is just one winner, I receive ___ _ €.
In the following we would like to know how you would have decided in case you would have been picked as a winner.
Otherwise: same questions as for A-winners.